Whitney categories and the Tangle Hypothesis

Conor Smyth; Jon Woolf

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arXiv · 1108.3724

Whitney categories and the Tangle Hypothesis

Conor Smyth·Jon Woolf

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Abstract

We propose a new notion of `n-category with duals', which we call a Whitney n-category. There are two motivations. The first is that Baez and Dolan's Tangle Hypothesis is (almost) tautological when interpreted as a statement about Whitney categories. The second is that we can functorially construct `fundamental Whitney n-categories' from each smooth stratified space X. These are obtained by considering the homotopy theory of smooth maps into X which are transversal to all strata. This makes concrete another idea of Baez and Dolan's which is that a suitable version of homotopy theory for stratified spaces should allow one to generalise the relationship between spaces and groupoids to one between stratified spaces and categories with duals.

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BibTeX RIS

Conor Smyth, Jon Woolf. 2011-08-18. Whitney categories and the Tangle Hypothesis. https://arxiv.org/abs/1108.3724

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